SUBROUTINE SAXPYI ( NZ, A, X, INDX, Y ) C C ================================================================== C ================================================================== C ==== SAXPYI -- INDEXED REAL ELEMENTARY VECTOR OPERATION ==== C ================================================================== C ================================================================== C C PURPOSE C ------- C C SAXPYI ADDS A REAL SCALAR MULTIPLE OF C A REAL SPARSE VECTOR X C STORED IN COMPRESSED FORM (X,INDX) C TO C A REAL VECTOR Y IN FULL STORAGE FORM. C C ONLY THE ELEMENTS OF Y WHOSE INDICES ARE LISTED IN INDX C ARE REFERENCED OR MODIFIED. THE VALUES IN INDX MUST BE C DISTINCT TO ALLOW CONSISTENT VECTOR OR PARALLEL EXECUTION. C C ALTHOUGH DISTINCT INDICES WILL ALLOW VECTOR OR PARALLEL C EXECUTION, MOST COMPILERS FOR HIGH-PERFORMANCE MACHINES WILL C BE UNABLE TO GENERATE BEST POSSIBLE CODE WITHOUT SOME C MODIFICATION, SUCH AS COMPILER DIRECTIVES, TO THIS CODE. C C ARGUMENTS C --------- C C INPUT ... C C NZ INTEGER NUMBER OF ELEMENTS IN THE COMPRESSED FORM. C A REAL SCALAR MULTIPLIER OF X. C X REAL ARRAY CONTAINING THE VALUES OF THE C COMPRESSED FORM. C INDX INTEGER ARRAY CONTAINING THE INDICES OF THE C COMPRESSED FORM. IT IS ASSUMED THAT C THE ELEMENTS IN INDX ARE DISTINCT. C C UPDATED ... C C Y REAL ARRAY, ON INPUT, WHICH CONTAINS THE C VECTOR Y IN FULL STORAGE FORM. ON OUTPUT C ONLY THE ELEMENTS CORRESPONDING TO THE C INDICES IN INDX HAVE BEEN MODIFIED. C C C SPARSE BASIC LINEAR ALGEBRA SUBPROGRAM C C FORTRAN VERSION WRITTEN OCTOBER 1984 C ROGER G GRIMES, BOEING COMPUTER SERVICES C C ================================================================== C C ------------- C ... ARGUMENTS C ------------- C INTEGER NZ, INDX (*) C REAL Y (*), X (*), A C C ------------------- C ... LOCAL VARIABLES C ------------------- C INTEGER I C C ================================================================== C IF ( NZ .LE. 0 ) RETURN C IF ( A .EQ. 0.0E0 ) RETURN C DO 10 I = 1, NZ Y(INDX(I)) = Y(INDX(I)) + A * X(I) 10 CONTINUE C RETURN END REAL FUNCTION SDOTI ( NZ, X, INDX, Y ) C C ================================================================== C ================================================================== C ==== SDOTI -- REAL INDEXED DOT PRODUCT ==== C ================================================================== C ================================================================== C C PURPOSE C ------- C C SDOTI COMPUTES THE VECTOR INNER PRODUCT OF C A REAL SPARSE VECTOR X C STORED IN COMPRESSED FORM (X,INDX) C WITH C A REAL VECTOR Y IN FULL STORAGE FORM. C C ONLY THE ELEMENTS OF Y WHOSE INDICES ARE LISTED IN INDX C ARE REFERENCED. C C ARGUMENTS C --------- C C INPUT ... C C NZ INTEGER NUMBER OF ELEMENTS IN THE COMPRESSED FORM. C X REAL ARRAY CONTAINING THE VALUES OF THE C COMPRESSED FORM. C INDX INTEGER ARRAY CONTAINING THE INDICES OF THE C COMPRESSED FORM. C Y REAL ARRAY, ON INPUT, WHICH CONTAINS THE C VECTOR Y IN FULL STORAGE FORM. ONLY C THE ELEMENTS CORRESPONDING TO THE C INDICES IN INDX WILL BE ACCESSED. C C OUTPUT ... C C SDOTI REAL REAL FUNCTION VALUE EQUAL TO THE C VECTOR INNER PRODUCT. C IF NZ .LE. 0 SDOTI IS SET TO ZERO. C C SPARSE BASIC LINEAR ALGEBRA SUBPROGRAM C C FORTRAN VERSION WRITTEN OCTOBER 1984 C ROGER G GRIMES, BOEING COMPUTER SERVICES C C ================================================================== C C ------------- C ... ARGUMENTS C ------------- C INTEGER NZ, INDX (*) C REAL X (*), Y (*) C C ------------------- C ... LOCAL VARIABLES C ------------------- C INTEGER I C C ================================================================== C SDOTI = 0.0E0 IF ( NZ .LE. 0 ) RETURN C DO 10 I = 1, NZ SDOTI = SDOTI + X(I) * Y(INDX(I)) 10 CONTINUE C RETURN END SUBROUTINE SGTHR ( NZ, Y, X, INDX ) C C ================================================================== C ================================================================== C ==== SGTHR -- REAL GATHER ==== C ================================================================== C ================================================================== C C PURPOSE C ------- C C SGTHR GATHERS THE SPECIFIED ELEMENTS FROM C A REAL VECTOR Y IN FULL STORAGE FORM C INTO C A REAL VECTOR X IN COMPRESSED FORM (X,INDX). C C ONLY THE ELEMENTS OF Y WHOSE INDICES ARE LISTED IN INDX C ARE REFERENCED. C C ARGUMENTS C --------- C C INPUT ... C C NZ INTEGER NUMBER OF ELEMENTS TO BE GATHERED INTO C COMPRESSED FORM. C Y REAL ARRAY, ON INPUT, WHICH CONTAINS THE C VECTOR Y IN FULL STORAGE FORM. ONLY C THE ELEMENTS CORRESPONDING TO THE INDICES C IN INDX WILL BE ACCESSED. C INDX INTEGER ARRAY CONTAINING THE INDICES OF THE C VALUES TO BE GATHERED INTO COMPRESSED FORM. C C OUTPUT ... C C X REAL ARRAY CONTAINING THE VALUES GATHERED INTO C THE COMPRESSED FORM. C C SPARSE BASIC LINEAR ALGEBRA SUBPROGRAM C C FORTRAN VERSION WRITTEN OCTOBER 1984 C ROGER G GRIMES, BOEING COMPUTER SERVICES C C ================================================================== C C ------------- C ... ARGUMENTS C ------------- C C INTEGER NZ, INDX (*) C REAL Y (*), X (*) C C ------------------- C ... LOCAL VARIABLES C ------------------- C INTEGER I C C ================================================================== C IF ( NZ .LE. 0 ) RETURN C DO 10 I = 1, NZ X(I) = Y(INDX(I)) 10 CONTINUE C RETURN END SUBROUTINE SGTHRZ ( NZ, Y, X, INDX ) C C ================================================================== C ================================================================== C ==== SGTHRZ -- REAL GATHER AND ZERO ==== C ================================================================== C ================================================================== C C PURPOSE C ------- C C SGTHRZ GATHERS THE SPECIFIED ELEMENTS FROM C A REAL VECTOR Y IN FULL STORAGE FORM C INTO C A REAL VECTOR X IN COMPRESSED FORM (X,INDX). C FURTHERMORE THE GATHERED ELEMENTS OF Y ARE SET TO ZERO. C C ONLY THE ELEMENTS OF Y WHOSE INDICES ARE LISTED IN INDX C ARE REFERENCED OR MODIFIED. C C ARGUMENTS C --------- C C INPUT ... C C NZ INTEGER NUMBER OF ELEMENTS TO BE GATHERED INTO C COMPRESSED FORM. C INDX INTEGER ARRAY CONTAINING THE INDICES OF THE C VALUES TO BE GATHERED INTO COMPRESSED FORM. C C UPDATED ... C C Y REAL ARRAY, ON INPUT, WHICH CONTAINS THE C VECTOR Y IN FULL STORAGE FORM. THE C GATHERED COMPONENTS IN Y ARE SET TO ZERO. C ONLY THE ELEMENTS CORRESPONDING TO THE C INDICES IN INDX HAVE BEEN ACCESSED. C C OUTPUT ... C C X REAL ARRAY CONTAINING THE VALUES GATHERED INTO C THE COMPRESSED FORM. C C SPARSE BASIC LINEAR ALGEBRA SUBPROGRAM C C FORTRAN VERSION WRITTEN OCTOBER 1984 C ROGER G GRIMES, BOEING COMPUTER SERVICES C C ================================================================== C C ------------- C ... ARGUMENTS C ------------- C INTEGER NZ, INDX (*) C REAL Y (*), X (*) C C ------------------- C ... LOCAL VARIABLES C ------------------- C INTEGER I C C ================================================================== C IF ( NZ .LE. 0 ) RETURN C DO 10 I = 1, NZ X(I) = Y(INDX(I)) Y(INDX(I)) = 0.0E0 10 CONTINUE C RETURN END SUBROUTINE SROTI ( NZ, X, INDX, Y, C, S ) C C ================================================================== C ================================================================== C ==== SROTI -- APPLY INDEXED REAL GIVENS ROTATION ==== C ================================================================== C ================================================================== C C ------------- C ... ARGUMENTS C ------------- C C PURPOSE C ------- C C SROTI APPLIES A GIVENS ROTATION TO C A SPARSE VECTOR X STORED IN COMPRESSED FORM (X,INDX) C AND C ANOTHER VECTOR Y IN FULL STORAGE FORM. C C SROTI DOES NOT HANDLE FILL-IN IN X AND THEREFORE, IT IS C ASSUMED THAT ALL NONZERO COMPONENTS OF Y ARE LISTED IN C INDX. ONLY THE ELEMENTS OF Y WHOSE INDICES ARE LISTED IN C INDX ARE REFERENCED OR MODIFIED. THE VALUES IN INDX MUST C BE DISTINCT TO ALLOW CONSISTENT VECTOR OR PARALLEL EXECUTION. C C ALTHOUGH DISTINCT INDICES WILL ALLOW VECTOR OR PARALLEL C EXECUTION, MOST COMPILERS FOR HIGH-PERFORMANCE MACHINES WILL C BE UNABLE TO GENERATE BEST POSSIBLE CODE WITHOUT SOME C MODIFICATION, SUCH AS COMPILER DIRECTIVES, TO THIS CODE. C C ARGUMENTS C --------- C C INPUT ... C C NZ INTEGER NUMBER OF ELEMENTS IN THE COMPRESSED FORM. C INDX INTEGER ARRAY CONTAINING THE INDICIES OF THE C COMPRESSED FORM. IT IS ASSUMED THAT C THE ELEMENTS IN INDX ARE DISTINCT. C C,S REAL THE TWO SCALARS DEFINING THE GIVENS C ROTATION. C C UPDATED ... C C X REAL ARRAY CONTAINING THE VALUES OF THE C SPARSE VECTOR IN COMPRESSED FORM. C Y REAL ARRAY WHICH CONTAINS THE VECTOR Y C IN FULL STORAGE FORM. ONLY THE C ELEMENTS WHOSE INDICIES ARE LISTED IN C INDX HAVE BEEN REFERENCED OR MODIFIED. C C C SPARSE BASIC LINEAR ALGEBRA SUBPROGRAM C C FORTRAN VERSION WRITTEN OCTOBER 1984 C ROGER G GRIMES, BOEING COMPUTER SERVICES C C ================================================================== C C ------------- C ... ARGUMENTS C ------------- C INTEGER NZ, INDX (*) C REAL X (*), Y (*), C, S C C ------------------- C ... LOCAL VARIABLES C ------------------- C INTEGER I C REAL TEMP C C ================================================================== C IF ( NZ .LE. 0 ) RETURN C IF ( ( C .EQ. 1.0E0 ) .AND. ( S .EQ. 0.0E0 ) ) RETURN C DO 10 I = 1, NZ TEMP = - S * X (I) + C * Y (INDX(I)) X (I) = C * X (I) + S * Y (INDX(I)) Y (INDX(I)) = TEMP 10 CONTINUE C RETURN END SUBROUTINE SSCTR ( NZ, X, INDX, Y ) C C ================================================================== C ================================================================== C ==== SSCTR -- REAL SCATTER ==== C ================================================================== C ================================================================== C C PURPOSE C ------- C C SSCTR SCATTERS THE COMPONENTS OF C A SPARSE VECTOR X STORED IN COMPRESSED FORM (X,INDX) C INTO C SPECIFIED COMPONENTS OF A REAL VECTOR Y C IN FULL STORAGE FORM. C C ONLY THE ELEMENTS OF Y WHOSE INDICES ARE LISTED IN INDX C ARE MODIFIED. THE VALUES IN INDX MUST BE DISTINCT TO C ALLOW CONSISTENT VECTOR OR PARALLEL EXECUTION. C C ALTHOUGH DISTINCT INDICES WILL ALLOW VECTOR OR PARALLEL C EXECUTION, MOST COMPILERS FOR HIGH-PERFORMANCE MACHINES WILL C BE UNABLE TO GENERATE BEST POSSIBLE CODE WITHOUT SOME C MODIFICATION, SUCH AS COMPILER DIRECTIVES, TO THIS CODE. C C ARGUMENTS C --------- C C INPUT ... C C NZ INTEGER NUMBER OF ELEMENTS TO BE SCATTERED FROM C COMPRESSED FORM. C X REAL ARRAY CONTAINING THE VALUES TO BE C SCATTERED FROM COMPRESSED FORM INTO FULL C STORAGE FORM. C INDX INTEGER ARRAY CONTAINING THE INDICES OF THE VALUES C TO BE SCATTERED FROM COMPRESSED FORM. C IT IS ASSUMED THAT THE ELEMENTS IN INDX C ARE DISTINCT. C C OUTPUT ... C C Y REAL ARRAY WHOSE ELEMENTS SPECIFIED BY INDX C HAVE BEEN SET TO THE CORRESPONDING C ENTRIES OF X. ONLY THE ELEMENTS C CORRESPONDING TO THE INDICES IN INDX C HAVE BEEN MODIFIED. C C SPARSE BASIC LINEAR ALGEBRA SUBPROGRAM C C FORTRAN VERSION WRITTEN OCTOBER 1984 C ROGER G GRIMES, BOEING COMPUTER SERVICES C C ================================================================== C C ------------- C ... ARGUMENTS C ------------- C INTEGER NZ, INDX (*) C REAL X (*), Y (*) C C ------------------- C ... LOCAL VARIABLES C ------------------- C INTEGER I C C ================================================================== C IF ( NZ .LE. 0 ) RETURN C DO 10 I = 1, NZ Y(INDX(I)) = X(I) 10 CONTINUE C RETURN END